JP Journal of Algebra, Number Theory and Applications
Volume 15, Issue 1, Pages 19 - 28
(October 2009)
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DECOMPOSITION OF MODULES
Hiroyuki Ishibashi (Japan)
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Abstract: Our first purpose is to give a sufficient condition for modules over rings to be expressed as a sum or a direct sum of submodules of the modules without any special restriction for modules and rings. Then we will apply the result to various cases of modules and rings.
For example, we will realize a generalization of the fact that an involutary endomorphism of a module gives rise to a splitting of the module into a direct sum of two submodules.
Also, we shall show that the existence of an idempotent linear endomorphism in a wide meaning allows us to split the underlying module. |
Keywords and phrases: decomposition of modules, direct sum of modules, annihilator ideal, involution, idempotent, structure theorem of finitely generated modules over PID, endomorphisms ring of modules, classical groups. |
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